where μi and σj are the sample mean and the sample standard deviation of the EMP
index of country j and νj,t+1are realisation of shocks to the EMP index and they are
obtained through 10000 draws from a standardised Gaussian distribution.
2. The second model is an optimal AR, which gives the following projection:
p
EMPjA,tR+1 = αkEMPjA,tR+1-k+σjνj,t+1 (8)
k=1
where the lag order p for the AR model specification is obtained through BIC . The
maximum order for the lags of the dependent variable, when using the BIC criterion,
has been fixed to four. We estimate σj using the standard deviation of the OLS
residuals from the estimation of the AR model. The scenarios associated with (??)
are obtained through 10000 draws from a standardised Gaussian distribution of the
idiosyncratic shock νj,t+1 .
3. The third class of models is given by an Autoregressive Distributed Lag model, ARDL:
K1 K2
EMPiA,tR+D1L = αk1EMPi,t+1-k1 + X αk2 exogj,t+1-k2 + σj νi,t+1 (9)
k1=1 k2=1
where the lag orders K1 and K2 are selected using recursive BIC (fixing the maximum
lag order to 4); exogj is the jth variable entering in the dataset x. The projection
equation (??) allows to assess whether current and past values of exogj improves upon
the AR, in terms of forecasting performance. The coefficients αk1 and αk2 are estimated
by recursive OLS, and the lag orders K1 and K2 are retrieved using the BIC criterion.
We estimate σj using the standard deviation of the OLS residuals from the estimation
of the ARDL model.The scenarios associated with (??) are obtained through 10000
draws from a standardised Gaussian distribution of the idiosyncratic shocks νj 4 .
It is important to observe that results either for the ARDL model specification with
principal components as regressors or for the models considered in this section would not
change if the Monte Carlo experiment is based upon draws from a Student t distribution
with k degrees of freedom5 . This would suggest that the DGP for the different EMP indices
at low frequency (given bi-annual observations) is well proxied by a Gaussian distribution.
4We have also treated exogj as stochastic when carrying the simulation experiment. This has been done
by adding to the last observation available at time t, that is exogjt , the realisation of a standard Gaussian
shock multiplied by its standard deviation. The latter is given by the sample standard deviation (using the
sample of observations ending at time t) of the jth variable in the dataset x. However, the empirical results
do not change.
5The associated with draws from Student t distribution with 3, 5, 10 degrees of freedom are available
upon request.